Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #29510210 | C2 | semidirect |
| 2. #29510206 | C2 | semidirect |
| 3. #29510205 | C2 | semidirect |
| 5. #29510195 | C2 | semidirect |
| 6. #29510194 | C2 | semidirect |
| 7. #29510180 | C2 | semidirect |
| 9. #29510174 | C2 | semidirect |
| 10. #29510173 | C2 | semidirect |
| 11. C2×C4⋊C4×C487 | C2 | semidirect |
| 72. C487 | #552 | semidirect |
| 84. C2×C4⋊C4 | D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29510210 | 2 |
| #29510206 | 2 |
| #29510205 | 2 |
| #29510198 | 2 |
| #29510195 | 2 |
| #29510194 | 2 |
| #29510180 | 2 |
| C4×C22⋊D487 | 2 |
| #29510174 | 2 |
| #29510173 | 2 |
| C2×C4⋊C4×C487 | 2 |
| #552 | 487 |